Numerical algorithm for nonlinear state feedback ℌ∞ optimal control problem

In this paper, the numerical algorithm based on conjugate gradient method to solve a finite-horizon min-max optimization problem arising in the ℌ_∞ control of nonlinear systems is presented. The feedback control and disturbance variables are formulated as a linear combination of basis functions. The proposed algorithm, which has a backward-intime structure, directly finds very accurate approximations of these feedbacks. Benchmark examples with analytic solutions are provided to demonstrate the effectiveness of the proposed algorithm.